1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ilya [14]
3 years ago
9

Problem 4 the measure of the largest angle of a triangle is 90◦ more than the measure of the smallest angle, and the measure of

the remaining angle is 30◦ more than the measure of the smallest angle. find the measure of each angle. showyourwork in obtaining your answe
Mathematics
1 answer:
azamat3 years ago
7 0
Answer:  The measurements of the angles are:  110° ;  50° ;  20°  .<span>
_________________________________________________________
Explanation:
________________________________________________________
Note:  There are 3 (three) angles in any triangle (by definition).

By definition, all the angles in any triangle add up to 180</span>° .<span>
________________________________________________________
The problems asks us to find the measure of EACH angle of the triangle.

We can set up an equation; given the information in the problem; to solve for the measure of EACH of the 3 (THREE) angles in the triangle:
________________________________________________________
     </span>→  " <span>x + (x + 90) + (x + 30) = 180 "  ;
_____________________________________________
   in which:  "x" is the measure of one of the angles;
                                (specifically, the smallest angle) in the triangle;
              "(x + 90)" is the measure of another one of the angles in the triangle; 
              </span>"(x + 30)" is the measure of another one of the angles in the triangle; <span>
___________________________________________________________
By solving for "x" in the equation; we can solve for the measures of all the angles in the triangle;
_________________________________________________
</span>  →   x + (x + 90) + (x + 30) = 180 ; 
<span>
         x + x + 90 + x + 30 = 180 ;
        
  </span>→<span>    3x + 120 = 180 ;
______________________________________
     Subtract "120" from each side of the equation ;

           3x + 120 </span>− 120 = 180 <span>− 120 ;
</span><span>
to get:      3x  = 60 ;
________________________________
   Now, divide EACH SIDE of the equation by "3" ; to isolate "x" on one side of the <span>equation ;  and</span> to solve for "x" ;

               3x = 60 ;
            
              3x / 3 = 60 / 3 ;
             
                 x = 20 ;
_________________________________________
Now, we have the original equation:
__________________________________
</span>x + (x + 90) + (x + 30) = 180 ; 
<span>
in which:  x = 20</span>° {the smallest angle) ; 
                "(x + 90)" = "(20 + 90) = 110° ;
                "(x + 30)" = "(20 + 30)" = 50° ;
<span>__________________________________________________________
Answer:  The measurements of the angles are:  110</span>° ;  50° ;  20°  .
<span>__________________________________________________________
To check our work:

20 + 110 + 50 =?  180 ?? ;   </span>→ 130 + 50 =?  180 ?? ; → Yes!
<span>_____________________________________________________

</span>
You might be interested in
Which data set could be represented by the box plot shown below?
Lapatulllka [165]

Answer:

The answer is C

Step-by-step explanation:

It starts at 25 and then it stops at 38.

I hope this helps!

6 0
2 years ago
Read 2 more answers
Find the perimeter of the figure below. <br><br> A) 42.1<br> B) 74.0<br> C) 84.2<br> D) 94.4
Andru [333]
The answer is C 84.2
6 0
3 years ago
Read 2 more answers
A rectangular lawn 70m by 50m has two cross roads each 6m wide running in the
ser-zykov [4K]
Area of road =70*50=3500
3500*2=7000 because it has cross road
6*6=36
7000-36=6964
6964*5.50=38302
6 0
2 years ago
Square ABCD is shown with four congruent images such that ABCD FGHI JKLM NOPQ RSTU.
N76 [4]

FGHI

Step-by-step explanation:

The square FGHI needs to be created into a reflection for true congruence of the figure thus transformed across the axis.

FGHI's co-ordinates' signs are to be reversed for reflection thus coordinates:

2,-5

4,-5

2,-7

4,-7

are made into

-2,5

-4,5

-2,7

-4,7

5 0
2 years ago
Read 2 more answers
The jug can hold 1500ml. The bucket can hold 2 litres. The barrel can hold 15 litres. Anisa wants to fill the barrel with water.
myrzilka [38]

Answer:

1. Using the jug 6 times and the bucket 3 times

2. Using the bucket 6 times, then using the jug two times

Step-by-step explanation:

Firstly, let’s remember that 1000 ml = 1l

Thus 2L = 2000 ml

And 15L = 15,000 ml

So the situation we are having now is that we want to fill a barrel of 15,000 ml using a jug of 1500 ml and a bucket with a capacity of 2000 ml

Firstly, the first way is using the bucket 6 times and the jug 2 times

What i mean by this is using the bucket 6 times bringing the total volume from the bucket as (6* 2000) = 12,000 ml

Then we are left with 15,000-12,000 = 3,000 ml

Now, she can fill the barrel with 2 times the full volume of the jug making 3,000

Secondly, she can also use the combination of both.

She can use the bucket 6 times and the jug 2 times

The total volume in each case here would be;

For the bucket; (2,000 * 6) = 12,000 ml

while for the jug, we have (1500 * 2) = 3,000 ml

And thus we shall be having a total of 12,000 + 3,000 = 15,000 ml this way

8 0
3 years ago
Other questions:
  • Find the product. Simplify, if needed. 2 1/8×1 1/6×3
    11·1 answer
  • Mark borrowed $53 from his parents for his graduation expenses. He paid $29. How much does Mark still owe
    6·1 answer
  • Karif plans to use a 20% coupon on a $27.60 purchase
    7·1 answer
  • For Matthew's lemonade recipe, 4 lemons are required to make 6 cups of lemonade. At what rate are lemons being used in cups of l
    8·1 answer
  • Suppose you know a certain parabola has a vertex of (2, 1) and a y-intercept of 4. By symmetry, you can conclude that the parabo
    8·1 answer
  • In parallelogram STUV, find the measure of TS.
    8·1 answer
  • Jennifer earned $1000 babysitting over the summer. She spent $250 of her earnings on new clothes. What percent of her earnings d
    10·2 answers
  • WHy Is ThIs oNe kAnSas bUt ThIs OnE iS nOt aRkAnsAs
    10·1 answer
  • In a correlational study, ____.
    5·1 answer
  • Answer as soon as possible pls
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!